Millennial parents are far more likely than their predecessors to save for their children's educations — and far more of them want to pay the whole tab for college.

Seventy-four percent of parents aged 30 to 34 polled for the 2015 Fidelity Investments College Savings Indicator have put aside money for college, compared to 58 percent of parents the same age who were polled in 2007.

Nearly half (48 percent) of the group born between 1981 and 1985 plan to pay for all college costs, compared with just 16 percent of parents the same age in 2007, according to the survey conducted for Fidelity by Boston Research Technologies.

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Millennial parents have spent much if not all of their adult lives living with the fallout from the financial crisis, says Keith Bernhardt, vice president of retirement and college products at Fidelity. That experience has made them determined to help their children avoid burdensome student loans. "They've seen the repercussions of taking on too much debt and the cost of that," he says.

Overall, the parents surveyed hope to pay for 66 percent of their children's college costs. Fidelity projects that based on current savings rates, they will be able to cover just 27 percent of projected college costs on average, Bernhardt says.

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Fidelity's survey does not represent the general population. Those surveyed were far more likely to have a college degree, for one thing.

The research firm interviewed 2,470 parents with children aged 18 and younger and household incomes over $30,000 a year or more. Among parents born between 1981 and 1997, 85 percent of those surveyed had attended college and 61 percent had college degrees.

The higher rates of education may explain why these parents are so gung-ho about helping their kids pay for college: they understand the benefit. An earlier Pew study found that 86 percent of college graduates felt their own education was a good investment, even as the majority of Americans (57 percent) said the higher education system fails to provide good value for the cost.

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While they may not be saving enough, the millennial parents polled have done many things right, Bernhardt says. The vast majority have put money aside monthly, and most (57 percent) started saving before their children turned six, compared to 47 percent of GenXers and 37 percent of Boomers.

Forty-three percent of millennials polled use 529 college savings plans to save (Fidelity just so happens to offer 529s), compared with 37 percent of GenX and Boomers.

One thing parents are still getting wrong, though, is being afraid that saving for college will hurt their kids' ability to get financial aid. Fidelity found 53 percent had that fear, even though money saved in a parent's name-such as in a 529-has only a small impact on aid. Financial aid formulas expect parents to use less than 6 percent of their non-retirement savings for college. Incomes factor far more into financial aid formulas than assets. "If you save $10,000, you'll lose just $600 in financial aid," Bernhardt says. "They want people to save."